Boundary Control for a General Class of
String Models

Objective

The chief objective behind this experiment is the control of an
undamped, nonlinear string with actuator dynamics at the boundary.

Background

Many different types of flexible mechanical systems exhibit
vibration in the presence of disturbances. One method for reducing
string vibration is to increase the cable tension; however, this
remedy induces high stresses which reduces the life of the cable.
Another method for reducing cable vibration is the application of
active boundary control via actuators. In this experiment we
develop a boundary controller which asymptotically stabilizes the
out-of-plane displacement. The control strategy developed removes
the need for knowing the exact structure of the nonlinear tension
function. The distributed mechanical model includes the dynamics
which naturally occur due to the mass of the requisite boundary
actuator. The controller requires the measurement of the slope (and
its time derivative) of the string at the actuated boundary, the
velocity of the string at the actuated boundary and the tension in
the string.

Experimental Setup

The proposed controller was implemented on a cable control system
designed and built in-house. An elastic nylon string, pinned at one
end, and connected to a horizontally-translating gantry at the
other end was used for the experiments. A brushed dc motor (Baldor
model 3300) was coupled to the gantry using a timing belt. A
1000-count rotary encoder (Hohner) was used to measure the gantry
position. A 4000-count rotary optical encoder mounted on the gantry
was used to measure the string departure angle while the JR3 Inc.
force-torque sensor mounted on at the pinned end measured the
tension in the string. A 586 ISA-based Pentium PC hosting a Quanser
Consulting MultiQ digital signal processing board served as the
computational engine.

The MultiQ board also supported two channels of 16-bit ADCs and
DACs. The angular velocity was obtained by applying a backwards
difference algorithm to the angle signal. To eliminate quantization
noise, the velocity signals were filtered using a second-order
digital filter. The six vectors from the JR3 processor unit (forces
along the 3 axes and moments along the 3 axes) were attained using
DMA. The Processor board was initialized using serial port
communication protocol. The control program (in C) was run in
Fumotor environment, an in-house s/w control-package. A graphical
user interface (GUI) aided the user to change control gains without
recompiling the program. A pair of limit switches (using proximity
sensors) were mounted at the two ends of the gantry path. These
prevented the gantry from hitting the limits. To test the response
of the proposed controller, the string was perturbed using a
gravity-based drop hammer. The hammer was allowed to hit the string
only once and always from the same height. This seemed to yield a
consistent input and therefore allowed for comparison between the
uncontrolled and controlled vibration of the string.

Experimental Setup

Another Point of View !

Experimental Results

Plots: Comparing the
Angular Displacements of Open Loop, Damper Control and Full Order
Knowledge Based Controllers(Plots will open in a new window)